Non-confluence for uncertain differential equations

Abstract

This paper is concerned with a class of non-linear uncertain differential equations driven by canonical process, which is the twin of Brownian motion in the structure of uncertain theory. By the Carathéodory approximation, we prove the existence and uniqueness of solutions for the considered equations under some non-Lipschitz conditions. Subsequently, By applying the chain rule for the considered equation, we introduce and attempt to explore the non-confluence property of the solution for the considered equation under some appropriate conditions. Our approach is to construct some suitable Lyapunov functions. Finally, two examples are provided to illustrate the effectiveness of our main results.